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PhoenixFire
Group Title
\[F(x)=\int _{ 1 }^{ ln(x^{ 2 }+e) }{ sin(e^{ t }) } dt\]
Find F'(x).
Not sure how to do this, I understand from the Fundamental Theorem of Calculus that
\[F'(x)=\frac { d }{ dx } \int _{ a }^{ x }{ f(t) } dt=f(x)\]
But what happens to the limit of \(ln(x^2+e)\)?
 one year ago
 one year ago
PhoenixFire Group Title
\[F(x)=\int _{ 1 }^{ ln(x^{ 2 }+e) }{ sin(e^{ t }) } dt\] Find F'(x). Not sure how to do this, I understand from the Fundamental Theorem of Calculus that \[F'(x)=\frac { d }{ dx } \int _{ a }^{ x }{ f(t) } dt=f(x)\] But what happens to the limit of \(ln(x^2+e)\)?
 one year ago
 one year ago

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bahrom7893 Group TitleBest ResponseYou've already chosen the best response.1
Don't you just do this: Sin(e^b)*(Sin(e^b)) ' where b is the upper limit.
 one year ago

bahrom7893 Group TitleBest ResponseYou've already chosen the best response.1
Well, you'd then subtract Sin(e^1) * (Sin(e^1))', but since the derivative of a constant is 0, this term becomes 0, and you're left with just the first one.
 one year ago

bahrom7893 Group TitleBest ResponseYou've already chosen the best response.1
Oh and by the way, e^(ln(x)) = x
 one year ago

PhoenixFire Group TitleBest ResponseYou've already chosen the best response.0
I don't understand why you're multiplying f(x) by f'(x) Or do you do the integration, and then derive it? \[\frac{d}{dx}(sin(e^{ln(x^2+e)})sin(e^1))=\frac{d}{dx}sin(x^2+e)=2xcos(x^2+e)=F'(x)\]
 one year ago
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